To compare the effectiveness of two treatments, researchers conducted a well-designed experiment using a randomized block design in which the subjects were blocked by age-group (under 40 years and 40 years or older). Which of the following must be true about the randomized block design of the experiment?
(A) The number of subjects in each block is different.
(B) Treatments are randomly assigned to subjects within each block.
(C) The design cannot have a control group because subjects are blocked by age-group.
(D) The experiment uses a matched-pairs design, where subjects from one block are paired with subjects from the other block.
(E) The subjects in one block receive one treatment, and the subjects in the other block receive the other treatment.

The vertex form of the quadratic function f(x) = 2x^2 + 8x + 7 is f(x) = 2(x + 2)^2 - 25.

Take a look at the quadratic function:

f(x) = 2x^2 + 8x + 7

In this situation, a = 2 and b = 8, yielding:

f(x) = 2(x^2 + 4x) + 7

It shtbe noted that to determine the value to add and subtract, multiply (b/2a)2 by (8/2(2))2 = 42 = 16. Inside the parenthesis, we add and subtract 16:

f(x) = 2(x^2 + 4x + 16 - 16) + 7

The expression inside the parenthesis can now be written as a perfect square:

f(x) = 2((x + 2)^2 - 16) + 7

Finally, the phrase is simplified by spreading the 2:

f(x) = 2(x + 2)^2 - 32 + 7

f(x) = 2(x + 2)^2 - 25

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What is the vertex form of the quadratic function f(x) = 2x^2 + 8x + 7

The area of the castle's floor increases by 5.06% .

How to calculate area of rectangular floor?

By multiplying length and breadth, the rectangle's area will obtain in a square-unit dimension. In the case of a square, the area will become side2. The main difference between square and rectangle is that the length and breadth are equal for square.

Given :

Let the Length and width of the rectangular floor be x and y respectively

then , the area of rectangular floor be x*y

Since,

Ashley increased the length of the castle's floor : 30%

and width of castle's floor : 20%.

New length = x + 30% of x = x + 3x/100 = 103x/100

New width = y + 20% of y =y + 2y/100 = 102y/100

New area of rectangular floor = (103x/100)*(102y/100)

percent increase in area of the castle's floor

= {[(103x/100)*(102y/100) - x*y]*100} / xy

= 506 / 100

= 5.06

Hence, the area of the castle's floor increases by 5.06% .

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Answer:

-6 -4

Step-by-step explanation:

Answer:

Solve the following:

a.  

b.  

c.

the answer is b

By changing the central angle, ∠CAB, the inscribed angle, ∠CDB has the following data sets:

m∠BAC (β)                                m∠BDC (α)

42°                                               84°

40°                                               80°

45°                                               90°

35°                                               70°

52°                                               104°

A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

In Geometry, a circle is considered to be a conic section which is formed by a plane intersecting a double-napped cone that is perpendicular to a fixed point (central axis) because it forms an angle of 90° with the central axis.

The inscribed angle theorem states that the measure of an inscribed angle is one-half the measure of the intercepted arc in a circle. Thus, this is given by this mathematical expression:

m∠BDC = ½ × m∠BAC.

For this exercise, we would change the central angle, ∠CAB, so that the inscribed angle, ∠CDB can have the following data sets:

m∠BAC (β)                                m∠BDC (α)

42°                                               84°

40°                                               80°

45°                                               90°

35°                                               70°

52°                                               104°

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Answer:

plato

Step-by-step explanation:

m∠BAC m∠BDC

50° 25°

70° 35°

90° 45°

125° 62.5°

150° 75°

The complete equation of the ellipse is \(\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1\)

The complete question is in the attachment

The given parameters are:

The vertex is represented as (h, k ± a).

So, we have:

h = -5

k + a = 14

k - a = -2

Add the last two equations

2k = 12

Divide by 2

k = 6

Substitute k = 6 in k + a = 14

6 + a = 14

Solve for a

a = 8

The ellipse equation is represented as:

\(\frac{(x - h)^2}{b^2} + \frac{(y - k)^2}{a^2} = 1\)

So, we have:

\(\frac{(x + 5)^2}{b^2} + \frac{(y - 6)^2}{8^2} = 1\)

The ellipse passes through the point (0,6).

So, we have:

\(\frac{(0 + 5)^2}{b^2} + \frac{(6 - 6)^2}{8^2} = 1\)

This gives

\(\frac{5^2}{b^2} + \frac{0}{8^2} = 1\)

Evaluate the quotient

\(\frac{5^2}{b^2} = 1\)

Cross multiply

\(b^2 = 5^2\)

Take the square root of both sides

b = 5

Substitute b = 5 in \(\frac{(x + 5)^2}{b^2} + \frac{(y - 6)^2}{8^2} = 1\)

\(\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1\)

Hence, the complete equation of the ellipse is \(\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1\)

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The answer to the question is 4/15

Answer:

please give my answer first

Answer:

408 is correct

0.8 x 510 = 408

Step-by-step explanation:

When we get a sale value or reduced value to find

This is a short cut of workings in bold to find correct value.

10% of 510 = 51

20% of 510 = 102

510-102 =408

17 x 30 = 510   Not correct as calculated before taxes.

100-80/ 100 = 0.8

0.8 x 510 = 408

408/510 = 0.8  Is correct

0(17) (30) = 510   Not correct as calculated before tax

510 - 2(17)(30) = 510 i Not correct as calculated before tax.

Answer:

x = 9

y = 9√3 = 15.6

Step-by-step explanation:

The triangle given is a right triangle, therefore:

✔️apply trigonometric ratio formula to find x:

Reference angle = 60°

Hypotenuse = 18

Adjacent = x

Thus:

Cos (60) = x/18

Multiply both sides by 18

18×cos(60) = x

9 = x

x = 9

✔️find y by applying pythagorean theorem:

y² = 18² - x² (pythagorean theorem)

y² = 18² - 9² (substitution)

y² = 243

y = √243

y = √(81*3)

y = 9√3 = 15.6

Answer:

-2(4 - 1)

Step-by-step explanation:

Choice A: ❌

9-(-17)

9 + 17 = 26

Choice B: ❌

(4 - 16)/(-2)

(-12)/(-2)

6

Choice C: ✅

-2(4 - 1)

-2(3)

-6

Choice D: ❌

3 x (-2) x (-1)

-6 x (-1)

6

Answer:

- 2(4 - 1)

Step-by-step explanation:

9 - (- 17)

9 + 17 = 26

\(\frac{4 - 16}{-2}\) = 12

- 2(4 - 1)

- 2(3) = - 6

3 × - 2 × - 1 = 6

If piece of cake has area of 100 in² and sweeps angle of 50°, then the radius of the cake is 15.13 inches.

The area of the piece of cake is given as 100 square inches and

The piece of cake sweeps out an angle of 50 degrees, we have to find the radius of the cake;

We know that "Area" of a sector of a circle is given as : A = (θ/360)πr²,

where A = area of the sector, θ is = angle swept by sector, and r is radius of circle,

We know that area of "piece-of-cake" is = 100 square inches and

The "angle-swept' by the piece is = 50 degrees.

Substituting the values in area of sector formula,

We get,

⇒ 100 = (50/360)πr²,

⇒ r² = (100 × 360)/(50π)

⇒ r ≈ 15.13,

Therefore, the radius of the cake is approximately 15.13 inches.

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Answer:

\(-\frac{4}{9}z\)-5

Step-by-step explanation:

You can only combine variables with like terms. Variables with like terms are \(\frac{7}{9} ( -\frac{6}{9} ) (-\frac{5}{9})\) so 7/9 - 6/9 is 1/9 and 1/9 - 5/9 is -4/9. The other variables with like terms are 2 and (-7). 2 - 7 = -5. Now combining these two together we get the fraction -4/9 -5

Answer:

center=(5,-3)

radius = 2 unit

Step-by-step explanation:

Scores between 23 & 59 will give Paul a C for the semester (an average between 70 and 79).

The sum of the scores on the first three, hundred point tests

= 82 + 88 + 87 = 257.

The total score required in four 100-point tests to get an average score of 70 = 70X4= 280.

The total score required in four 100-point tests to get an average score of 79 = 79X4= 316.

Therefore, the score on the fourth test should be between (280-257) & (316-57) i.e, 23 & 59 to get an average score of 70 & 79.

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Answer:

46−5y

Step-by-step explanation:

5(10−y)−4

Use the distributive property to multiply 5 by 10−y.

50−5y−4

Subtract 4 from 50 to get 46.

46−5y

Graph if needed:

Answer:

46 - 5y

Step-by-step explanation:

5(10-y)-4

50 - 5y - 4

= 46 - 5y

Answer:

hlp

Step-by-step explanation:

hlp

Answer: Yes, there is an outlier of 45, This means that one person's age was 45, which is 25 years younger than the next closest age.

Hope this helps! :)

Step-by-step explanation:

Answer:

D

GIVE HIME BRAINLIEST

Step-by-step explanation:

Step-by-step explanation:

Hope this helps you... Lemme know if you don't understand

Answer:

m <5=91 is the correct response to this question

1. The average daily balance for this credit card account is $187.74.

2. The finance charge for the month of April is $249.22.

The average daily balance for April is the total of the balance for every day in the billing cycle divided by the number of days in the billing cycle.

A billing cycle for a credit card account is usually one month.

Interest rate = 16.15% compounded monthly

Date       Activity            Amount     Balance  

April 1    Beginning Balance          $1,000.00

April 5   Purchase           29.10         1,029.10

April 12  Payment      −225.00           804.10

April 15  Purchase         97.25            901.35

April 23 Purchase         19.00           920.35

April 26 Purchase        28.40           948.75

April 30 Ending Balance                  948.75

Total                                            $5,632.05

Average daily balance = $187.735 ($5,632.05/30 days)

Daily interest rate = 0.04425 (16.15%/365)

Finance charge = $249.22 ($187.74 x 0.04425 30 days)

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Answer:

Class width = 20

Approximate lower class limit of the first class = 110

Approximate Upper class limit of the first class = 119

Step-by-step Explanation:

The class width of the histogram attached below can be gotten by finding the difference between successive lower class limits.

Thus, class width = 130 - 110 = 20

The approximate lower class limit of the first class is the lowest score we have in the first class = 110

The approximate upper class limit of the first class is the closest highest score that fall within the first class and is below the lower limit of the second class. Thus approximate upper class limit of the first class = 129

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

The option that represents shapes of the sampling distribution of p hat  is:

c. Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10 , the sampling distribution of p hat is not approximately Normal. Because p = 0.87 is closer to 1 than 0, the sampling distribution of p hat is skewed to the left.

Normal distribution is defined as the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

Because the requirement for normal is greater than 10, n×p is greater than 10 and nx(1-p) is also greater than 10.

This situation is abnormal because it is not valid. If p is close to 1 in a normal graph, then p is left skewed.

Thus, the option third is correct because nx(1-p)=2.6 less than equal to 10 then the sampling distribution  is not approximate normal because p=0.87 is closer to 1 than zero. Sampling distribution  is skewed to the left.

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The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Answer:

B

Step-by-step explanation:

using the recursive rule \(a_{n}\) = 3\(a_{n-1}\) and a₁ = 10, then

a₁ = 10

a₂ = 3a₁ = 3 × 10 = 30

a₃ = 3a₂ = 3 × 30 = 90

the first 3 terms are 10 , 30 , 90

Hey there! I'm happy to help!

Let's say that we don't have jokers. In that case, there are 52 cards, and half of them are red (so 26 are red). The probability of pulling a red card once is 1/2 since half the cards are red.

If we pick one out, there are only 51 total cards left and 25 red cards. So, the probability of picking one again would be 25/51.

We multiply the probabilities of these two events to find the probability of them both happening.

1/2×25/51=25/102

The probability of picking two red cards in a row is 25/102 or around 24.5%.

Have a wonderful day! :D

Answer: Number 2

Step-by-step explanation: yes